Show that the minimum value of `(x+a)(x+b)//(x+c)dotw h e r ea > c ,b > c ,` is `(sqrt(a-c)+sqrt(-c))^2` for real values of `x >-cdot`

Explanation

Given expression is `(x + a) (x + b) //(x + c).`
Let `x + c + y `. Then
`((x + a) (x + a))/((x + c)) = ((y+ (a - c))(y+(b-c)))/(y)`
` = (y^(2)+ [(a - c)+(b -c)]y+(b-c)(b - c))/(y)`
` = y+((a - c)+(b -c))/y+(b-c)+(b - c)`
`=[sqrt(y)-sqrt((a-c)(b-c))/(y)]^(2) + [sqrt(a-c)+sqrt(b-c)]^(2)`
` =ge[sqrt(a - c)+sqrt(b -c)]^(2)`
Hence, the least value is `[sqrt(a - c)+sqrt(b -c)]^(2)`